Everything is fine now, as you can see there is nothing to do message, meaning your system is up to date.
The other information about nemo dropbox means that you’re using the arch linux version (newer) than antergos one, but it’s fine.

I’ve gone through all the commands you suggested in the other topic, but I still get the message. I can open the file stored in /var/cache/pacman/pkg and extract it without any problems or error. I really don’t understand it.

…I can open the file stored in /var/cache/pacman/pkg and extract it without any problems or error. I really don’t understand it.

This is an answer to the final part of the post only.

In repos what is called a package is actually consists of two physical files:

package-name.pkg.tar.xz <-- the package itself

package-name.pkg.tar.xz.sig <-- the package signature

Before downaloading from a repo, pacman checks a package with its signature. It is done to verify that the package is correct.

After that, only a package itself is downloaded on a local computer. A package’s signature is not downloaded. There are no package-name.pkg.tar.xz.sig files in /var/cache/pacman/pkg folder.

It is assumed that locally stored packages are already checked with their signatures. There’s no need to run a signature check for them a second time.

So it is not only possible to extract local packages with an archive manager (Engrampa in Mate), but also directly install them with pacman. Pacman doesn’t perform a signature check for locally stored packages.

As to the main question, try to change your mirrors. antergos/nemo-dropbox lives in the [antergos] repo, and its mirrors are listed in the /etc/pacman.d/antergos-mirrorlist file. Simply try to change the repos order in it.